Daniel:
This is more of a philosophical question. I will address it as such. So, there exists something known as the Peano-Dedekind axioms in mathematical logic, from which we get our sense of enumeration. For starters, let us define a set that is empty, that has nothing in it. We call that the empty or void set and is denoted by a lowercase greek letter phi or 0 with a line through it. From here, then we can begin our construction of the integers, with just the empty set and something that is called the 'successor' function. Plain and simple, it is just succ(x) = x U {x} . With this and the empty set, we then proceed to the 'successor' of the empty set, which is the set that contains the empty set. In set-theoretic notation, this is succ(0#) = 0# U {0#}. This is equivalent to the set { #0}, the set containing the empty set. Another implementation gives succ({#0}) = {#0} U {{#0}} , which is equivalent to the set that contains the set containing the empty set. According to Peano arithmetic, this set is what corresponds to the definition of '2'. I hope this gives you some intuition on the 'why' and feel free to ask me on other things, i.e. how do we define addition or why 2 + 3 really is 5.
This is more of a philosophical question. I will address it as such. So, there exists something known as the Peano-Dedekind axioms in mathematical logic, from which we get our sense of enumeration. For starters, let us define a set that is empty, that has nothing in it. We call that the empty or void set and is denoted by a lowercase greek letter phi or 0 with a line through it. From here, then we can begin our construction of the integers, with just the empty set and something that is called the 'successor' function. Plain and simple, it is just succ(x) = x U {x} . With this and the empty set, we then proceed to the 'successor' of the empty set, which is the set that contains the empty set. In set-theoretic notation, this is succ(0#) = 0# U {0#}. This is equivalent to the set { #0}, the set containing the empty set. Another implementation gives succ({#0}) = {#0} U {{#0}} , which is equivalent to the set that contains the set containing the empty set. According to Peano arithmetic, this set is what corresponds to the definition of '2'. I hope this gives you some intuition on the 'why' and feel free to ask me on other things, i.e. how do we define addition or why 2 + 3 really is 5.
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Hello Daniel P, 2 is just one more 1 and just one less than 3. It is the average value of 6 and -2.
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2 is two. And is the number between 1 and 3
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2
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2